Instead of building a new desktop, I was told somewhere in these very forums that it is better if I get an external (larger) monitor and a USB hub. I already have an idea for the USB 3.0 hub I want. I am looking at this monitor as the one to get. Given that my notebook outputs to HDMI and VGA, this should work OK.

Is there a better monitor to output to, given a $400 budget? And can my HP laptop output to that top resolution the monitor allows?

It's unlikely the HDMI port in your laptop can support the top resolution of the linked monitor, and I've not been able to find any documentation indicating it can do anything greater than 1920*1080. You'd be better off buying a 1920*1080 monitor if you want to be sure.

For almost $100 less, suggest sticking with one of the many 27-inch IPS monitors that supports HDMI and can do 1920x1080, such as this Asus here (or alternately, here). Besides the possible technical limitations of your laptop's HDMI port, as already noted, the 27-inch unit will probably be a better tradeoff in terms of usability.

FWIW I'm using a 27" IPS LED with a similar panel (AOC branded, cheap Black-Friday special from Best Buy last November) and have no complaints about size and resolution. For example, I can open two document programs -- say, a PDF reader and Word -- side by side and work between both concurrently. And unless you happen to watch ultra-wide-encoded video regularly, most HD source material will use all or most of the display.